Physical Sciences and Mathematics Commons^™

Dynamics Of Conformal Maps For A Class Of Non-Laplacian Growth Phenomena, Martin Z. Bazant, Jaehyuk Choi, Benny Davidovitch

Benny Davidovitch

Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro- migration. Both continuous and stochastic dynamics are described by generalizing conformal- mapping techniques for viscous fingering and diffusion-limited aggregation, respectively. A gen- eral notion of time in stochastic growth is also introduced. The theory is applied to simulations of advection-diffusion-limited aggregation in a background potential flow. A universal crossover in mor- phology is observed from diffusion-limited to advection-limited fractal patterns with an associated crossover in the growth rate, controlled by a time-dependent effective Peclet number. …